When receiving a typical MR exam, a patient may expect to lie in the MR scanner for as long as 45 min or so. During this time, the anatomy of interest gets repeatedly imaged, using a variety of tissue contrasts. To visualize any image feature there needs to be significant contrast between this feature and background tissues, and acquiring images of different contrast improves the odds of being able to visualize diagnostically- relevant features. The presently-proposed approach allows the main MR properties that determine contrast to be rapidly and quantitatively evaluated, so that any desired contrast might subsequently be computed rather than acquired. From data acquired in just a few minutes, the present method aims to generate 3D maps of all of the main physical MR parameters: The relaxation times T1, T2 and T2*, the equilibrium magnetization M0, the flip angle and the offset frequency ?f. A major strength of the approach described here is that the various MR parameters are evaluated one at a time and/or through linear equations, as opposed to numerically solving larger and non-linear systems of equations involving many or all parameters at once. As few as two MR data sets may be acquired, using different flips angles, a1 and a2, and/or different repetition times, TR1 and TR2. While timing parameters such as TR are precisely known, the flip angle, on the other hand, varies spatially. From the center of the imaged volume where it is approximately equal to the user-requested value, the flip angle progressively decreases all the way to zero at the edges of the excited region in ways that are object-dependent. For this reason, a1 and a2 must be thought of as variables to be measured and evaluated rather than known imaging parameters. Based on MR parameter maps, 3D images of essentially any MR contrast can be computed rather than acquired, and new types of contrast can even be invented. The proposed few-minute 3D acquisition might potentially replace a whole exam. If successful, the method could be used for screening: For a very affordable cost one might purchase a few-minute passage into a scanner, nobody should die of tumors discovered too late. Furthermore, the proposed approach may help accelerate the transition of MRI from a mostly qualitative to a quantitative modality, as clinicians in time may grow to prefer looking at MR quantitative maps rather than qualitative contrasts. The present high-risk-high-reward project involves tailoring the proposed 3D quantitative mapping approach for head and joint (knee) imaging. The ability of the method to generate quantitative maps as well as synthetic images of common contrast types will be validated in phantoms, volunteers and patients. For both the head and the knee application, a main goal of the project is to obtain 3D images of diagnostic quality from five different healthy volunteers in a same 45 minute exam, to demonstrate the potential of the approach as a fast screening method.